Full identifiability of independent mechanism analysis

Establish whether independent mechanism analysis, which constrains the columns of the Jacobian of a nonlinear mixing diffeomorphism to be orthogonal without using an observed auxiliary variable, delivers full identifiability.

Background

The paper surveys nonlinear extensions of independent component analysis in which the linear mixing matrix is replaced by a diffeomorphism. Without additional structure, such nonlinear mixtures are generally non-identifiable, so independent mechanism analysis imposes geometric constraints on the Jacobian of the mixing map.

The cited result excludes the classical Darmois constructions without an auxiliary variable, but the paper explicitly notes that full identifiability has not been established under this geometric restriction alone.